On the numerical reliability of nonsmooth autodiff: a MaxPool case study
Abstract: This paper considers the reliability of automatic differentiation for neural networks involving the nonsmooth MaxPool operation across various precision levels (16, 32, 64 bits), architectures (LeNet, VGG, ResNet), and datasets (MNIST, CIFAR10, SVHN, ImageNet). Although AD can be incorrect, recent research has shown that it coincides with the derivative almost everywhere, even in the presence of nonsmooth operations (such as MaxPool and ReLU). On the other hand, in practice, AD operates with floating-point numbers, and there is, therefore, a need to explore subsets on which AD can be {\em numerically} incorrect. These subsets include a bifurcation zone (where AD is incorrect over reals) and a compensation zone (where AD is incorrect over floating-point numbers but correct over reals). Using SGD for the training process, we study the impact of different choices of the nonsmooth Jacobian for the MaxPool function on the precision of 16 and 32 bits. These findings suggest that nonsmooth MaxPool Jacobians with lower norms help maintain stable and efficient test accuracy, whereas those with higher norms can result in instability and decreased performance. We also observe that the influence of MaxPool's nonsmooth Jacobians on learning can be reduced by using batch normalization, Adam-like optimizers, or increasing the precision level.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Yunwen_Lei1
Submission Number: 2280
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